1) In the lesson "Looking at an Angle", Mrs. Sanchez teaches her 7th graders about angles. She begins the lesson by taking the students outside to look at the angles a ladder makes. This type of teaching connects to the real world and allows the students to relate. Back in the classroom, the students do activities that relate to angles, height and distance ratios. Students work together in small groups to determine angle measurements and height to distance ratios as well as plotting a graph. The lesson is all connected to the ladder and what angle is needed in order to it to be safe to use.
2) I saw many process standards demonstrated throughout this lesson. The process standards that stood out to me were communication, connections, and problem solving. Communication was demonstrated by having the students work in groups and with partners to solve problems and work together. The students then had to communicate as a whole class in order to plot the graph with all of the angle measurements. Making connections was demonstrated throughout the entire lesson because the concept of measuring the angle of a ladder automatically made a connection with the students. The students were using real life angles and real life scenerios to solve problems. The students felt connected to this math problems because they were determining if the ladder was safe to use. The students also demonstrated problem solving when they worked in partners and small groups in order to figure out different measurements. The students were only given certain numbers, either the angle or the height and distance, and had to figure out the opposite by problem solving. The students then had to determine if these measurements would be safe for the ladder.
I saw many of the Standards of Mathematical Practice being demonstrated throughout these video clips. The three standards that stook out most to me were make sense of problems and persevere in solving them, use appropriate tools strategically and model with mathematics. The students make sense of problems and persevere in solving them by working together to solve the problems, understand the different approaches to the problem, and understand the effects that are involved. The students use appropriate tools strategically when using their protractors and compasses to measure angles. The students model with mathematics when connecting the measurement of angles to the placement of ladders and using real life scenerios.
3) I thought the lessons in the video clips was very engaging and well planned. The concept of the lesson I thought was a great idea and really got the students interested in the topic of angles. Since they know a purpose for measuring angles they got more excited about it. I liked how the students worked with partners and small groups to continue measuring angles and height and distances. I also thought the teacher was well organized and liked her direct instructions. She had guided questions that helped the students along, yet it was no obvious. I also liked that the videos also gave a script of what the teacher and students were saying, it was easy to follow.
Tuesday, February 28, 2012
Thursday, February 9, 2012
Review of Math Applets
Grades 3-5
5.2 Understanding distance, speed, and time relationships using simulation software
http://www.nctm.org/standards/content.aspx?id=25037
This applet simulates two runners running along a track. Students control the speed and the starting points, they can then replay it and see a graph viewing the time-distance relationship. The objective states that this will help students understand ideas about functions and representing change over time. This applet is pretty easy to use, with reading the directions first. I did not read the directions first and I was confused, after going back and reading the step by step directions given, it was a simple simulation to use. The visual presentation and graphics are not great, but they get the point across. This applet could have been a lot more visually pleasing by having better graphics and more detail.
I think this applet overall would be beneficial for students to learn from. Although, I did not think it is the more graphically pleasant applet, the content is good. This applet allows students to be the controller and change the speed, the way the runner is facing, the amount of steps the runner takes, the starting position the runner takes, and how fast or slow the runner goes. Automatically, all the information is relayed on a graph that displays both runners and whatever information the student enters. I think there are great follow up questions and tasks for the students. An example of an additional question, that can be an interdisciplinary lesson, is: Set the starting position and length of stride for both runners. Run the simulation. Now write a story that describes the trip. For example, "The girl is going really fast. She catches up to and passes the boy, who is going slow," or "The girl started way behind the boy, who was already halfway to the tree by the time she got going. She went really fast and caught up to him more and more. Finally, at 75 she passed him and kept going really fast and got to the tree first." Although there is no set assessment, you could use any of the questions as an assessment, as they all involve the applet and knowing how to use it.
There are also great follow up reflection questions for the teacher as well. Some of the reflections include: Do you think the students would enjoy using this activity? And what important ideas about functions and representing change over time will the students get out of this activity?
5.1 Communicating about mathematics using games
5.1.1 Playing Fraction Tracks
http://www.nctm.org/standards/content.aspx?id=26975
This applet supports students' learning about fractions. The objective stated is students have opportunities to think about fractions and how they relate to a unit whole, compare fractional parts of a whole, and find equivalent fractions. This applet is extremely easy to use and is self explanatory. This applet is designed to be done in partners, however, it could work with just one person as well. Each player gets a fraction and they have to find fractions that can make it, or find the fraction on the board. Since this is also from the NCTM website, it is made similarly to my previous applet. It is not visually pleasing either, and the graphics are not very good. Once again, while the graphics are not as pleasing as they could be, the content is still good. This would not be an applet to use for a lesson, but more so if the students have extra time or need additional help with fractions. Other than the actually game through the applet, there is no assessment. There are no additional tasks or questions other than: To extend this game, students could make their own boards with different fractions, with decimals, or with a combination of decimals and fractions.
There are reflective questions for the teacher once again, such as How can playing this sort of game help children build understanding of equivalent fractions?
Like I said, this would not be an applet I would introduce my class to for a lesson. This would be more of a "filler" or something for students to do if they have extra time or need additional help in fractions.
5.2 Understanding distance, speed, and time relationships using simulation software
http://www.nctm.org/standards/content.aspx?id=25037
This applet simulates two runners running along a track. Students control the speed and the starting points, they can then replay it and see a graph viewing the time-distance relationship. The objective states that this will help students understand ideas about functions and representing change over time. This applet is pretty easy to use, with reading the directions first. I did not read the directions first and I was confused, after going back and reading the step by step directions given, it was a simple simulation to use. The visual presentation and graphics are not great, but they get the point across. This applet could have been a lot more visually pleasing by having better graphics and more detail.
I think this applet overall would be beneficial for students to learn from. Although, I did not think it is the more graphically pleasant applet, the content is good. This applet allows students to be the controller and change the speed, the way the runner is facing, the amount of steps the runner takes, the starting position the runner takes, and how fast or slow the runner goes. Automatically, all the information is relayed on a graph that displays both runners and whatever information the student enters. I think there are great follow up questions and tasks for the students. An example of an additional question, that can be an interdisciplinary lesson, is: Set the starting position and length of stride for both runners. Run the simulation. Now write a story that describes the trip. For example, "The girl is going really fast. She catches up to and passes the boy, who is going slow," or "The girl started way behind the boy, who was already halfway to the tree by the time she got going. She went really fast and caught up to him more and more. Finally, at 75 she passed him and kept going really fast and got to the tree first." Although there is no set assessment, you could use any of the questions as an assessment, as they all involve the applet and knowing how to use it.
There are also great follow up reflection questions for the teacher as well. Some of the reflections include: Do you think the students would enjoy using this activity? And what important ideas about functions and representing change over time will the students get out of this activity?
5.1 Communicating about mathematics using games
5.1.1 Playing Fraction Tracks
http://www.nctm.org/standards/content.aspx?id=26975
This applet supports students' learning about fractions. The objective stated is students have opportunities to think about fractions and how they relate to a unit whole, compare fractional parts of a whole, and find equivalent fractions. This applet is extremely easy to use and is self explanatory. This applet is designed to be done in partners, however, it could work with just one person as well. Each player gets a fraction and they have to find fractions that can make it, or find the fraction on the board. Since this is also from the NCTM website, it is made similarly to my previous applet. It is not visually pleasing either, and the graphics are not very good. Once again, while the graphics are not as pleasing as they could be, the content is still good. This would not be an applet to use for a lesson, but more so if the students have extra time or need additional help with fractions. Other than the actually game through the applet, there is no assessment. There are no additional tasks or questions other than: To extend this game, students could make their own boards with different fractions, with decimals, or with a combination of decimals and fractions.
There are reflective questions for the teacher once again, such as How can playing this sort of game help children build understanding of equivalent fractions?
Like I said, this would not be an applet I would introduce my class to for a lesson. This would be more of a "filler" or something for students to do if they have extra time or need additional help in fractions.
Tuesday, February 7, 2012
Journal Summary 2
The Value of Debts and Credits
Akyuz, D. (2012). The value of debts and credits. Mathematics Teaching in the Middle School, 17(5), 332-338.
Certain teaching practices can support students' mathematical reasoning. The topic in this article is integers, which are typically a challenge in the mathematical community. A persons financial net worth provided the context for the activities in this article. The integer operations used were addition, subtraction, and multiplication. This type of instruction is realistic mathematical education (RME). This type of instruction allows students to use their informal knowledge of mathematics and progress to move towards formal mathematical reasoning. There is a detailed chart in this article that explains how to foster mathematical reasoning. The article is based off of a study done over a five week period in a 7th grade classroom in Central Florida. There were 20 students, 13 boys and 7 girls, 3 students had mild learning disabilities. The data included teacher interviews, audio and video taped classroom sessions, field notes, teacher notes, research meetings, and a collection of student work. The most important practices that have been found to support student reasoning involved: encouraging students to give concrete explanations to think of effective solutions, to make conjectures and prove them, and to provide different and sophisticated solutions. The article demonstrates how an expert teacher incorporates these practices into her teaching. Although this lesson focuses on debts and assets it can be modified to fit other topics. The article then gives a description of the practices and provides classroom examples. Teachers need to know hot to support students mathematical reasoning from concrete to abstract, to motivate, support, and give opportunities to explore mathematical reasoning and concepts.
I thought this article had some really good ideas for including mathematical reasoning into the classroom. I do not recall doing anything like this when I was in middle school, however, times change. I think that including real life scenarios to teach a math lesson is a great idea and is extremely beneficial to the students. The students feel that it is actually knowledge they need to know, therefore, they will be more enthusiastic and take an interest in the lesson. Personally, I thought thought the wording throughout the article was a little heavy. I am use to reading articles and journals geared toward primary grades, since that is what I would like to teach. This article, geared towards middle school grades, had a lot more wording and mathematical vocabulary that I am not use to. I was not familiar with these practices and so I found this article to be a learning experience for me.
Akyuz, D. (2012). The value of debts and credits. Mathematics Teaching in the Middle School, 17(5), 332-338.
Certain teaching practices can support students' mathematical reasoning. The topic in this article is integers, which are typically a challenge in the mathematical community. A persons financial net worth provided the context for the activities in this article. The integer operations used were addition, subtraction, and multiplication. This type of instruction is realistic mathematical education (RME). This type of instruction allows students to use their informal knowledge of mathematics and progress to move towards formal mathematical reasoning. There is a detailed chart in this article that explains how to foster mathematical reasoning. The article is based off of a study done over a five week period in a 7th grade classroom in Central Florida. There were 20 students, 13 boys and 7 girls, 3 students had mild learning disabilities. The data included teacher interviews, audio and video taped classroom sessions, field notes, teacher notes, research meetings, and a collection of student work. The most important practices that have been found to support student reasoning involved: encouraging students to give concrete explanations to think of effective solutions, to make conjectures and prove them, and to provide different and sophisticated solutions. The article demonstrates how an expert teacher incorporates these practices into her teaching. Although this lesson focuses on debts and assets it can be modified to fit other topics. The article then gives a description of the practices and provides classroom examples. Teachers need to know hot to support students mathematical reasoning from concrete to abstract, to motivate, support, and give opportunities to explore mathematical reasoning and concepts.
I thought this article had some really good ideas for including mathematical reasoning into the classroom. I do not recall doing anything like this when I was in middle school, however, times change. I think that including real life scenarios to teach a math lesson is a great idea and is extremely beneficial to the students. The students feel that it is actually knowledge they need to know, therefore, they will be more enthusiastic and take an interest in the lesson. Personally, I thought thought the wording throughout the article was a little heavy. I am use to reading articles and journals geared toward primary grades, since that is what I would like to teach. This article, geared towards middle school grades, had a lot more wording and mathematical vocabulary that I am not use to. I was not familiar with these practices and so I found this article to be a learning experience for me.
Monday, February 6, 2012
Journal Summary 1
The Big Picture: Examine the Structure of CCSSM and Consider Major Ideas That Will Influnce Their Implementation.
This article is an introduction to a series of five articles to support implementing the CCSSM. Future articles will address additional topics, ideas, and different grade bands.
The article introduction the idea of the standards and gave some background information about the CCSSM. This will be the first time in US history that a set of standards is established and taught in nearly every state, 44 states have currently adopted the standards. These standards introduce a significant change in the way we teach mathematics. This article provides an overview of CCSSM by addressing four main parts: 1.) Describe the standards which apply to K-12. 2.) Describe the parts of the grade level standards. 3.) Explain how the standards develop across grade levels 4.) Discuss the intersection of the domains of the CCSSM.
The article further explains what the eight standards are, and then explains the grade-level standards. The grade-level standards include a 2 page introduction describing the critical areas and broad clusters for each grade, supplying teachers with essential ideas to focus on throughout the year. The teachers can sort the different standards into categories such as: standards they are ready to implement, standards they have some ability to implement, and those that need the most preparation to implement. Also provided in the article is a list of questions the educators and districts get to begin conversations that lead to strong advocacy of the CCSSM. Throughout the article there are examples, tables, and pictures explaining and describing how to read and understand the different sections of the CCSSM.
As a future educator, I found this article incredibly helpful. This article is specifically designed to instruct educators on how to use the CCSSM in their classrooms and how to understand the standards themselves. Since this is the first of a series of five, I'm sure the other articles will go more into specific examples with different grade levels and so forth. Personally, this is an article that I would like to read especially if I was confused or overwhelmed with not knowing how to incorporate the standards into my lessons. It gives step by step instructions and definitions on how to use the standards and what the standards are. This would be an article, or series of articles, to refer back to once I have a classroom of my own.
This article is an introduction to a series of five articles to support implementing the CCSSM. Future articles will address additional topics, ideas, and different grade bands.
The article introduction the idea of the standards and gave some background information about the CCSSM. This will be the first time in US history that a set of standards is established and taught in nearly every state, 44 states have currently adopted the standards. These standards introduce a significant change in the way we teach mathematics. This article provides an overview of CCSSM by addressing four main parts: 1.) Describe the standards which apply to K-12. 2.) Describe the parts of the grade level standards. 3.) Explain how the standards develop across grade levels 4.) Discuss the intersection of the domains of the CCSSM.
The article further explains what the eight standards are, and then explains the grade-level standards. The grade-level standards include a 2 page introduction describing the critical areas and broad clusters for each grade, supplying teachers with essential ideas to focus on throughout the year. The teachers can sort the different standards into categories such as: standards they are ready to implement, standards they have some ability to implement, and those that need the most preparation to implement. Also provided in the article is a list of questions the educators and districts get to begin conversations that lead to strong advocacy of the CCSSM. Throughout the article there are examples, tables, and pictures explaining and describing how to read and understand the different sections of the CCSSM.
As a future educator, I found this article incredibly helpful. This article is specifically designed to instruct educators on how to use the CCSSM in their classrooms and how to understand the standards themselves. Since this is the first of a series of five, I'm sure the other articles will go more into specific examples with different grade levels and so forth. Personally, this is an article that I would like to read especially if I was confused or overwhelmed with not knowing how to incorporate the standards into my lessons. It gives step by step instructions and definitions on how to use the standards and what the standards are. This would be an article, or series of articles, to refer back to once I have a classroom of my own.
Dacey, L., & Polly, D. (2012). Common core standards for mathematics: The big picture. Teaching Children Mathematics, 18(6), 378-383.
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